First of all the 22 day pass in one month costs less than 938$. About 750$ CDN if you take today's exchange rate (~x1.5). Also this is the rate for adults, but if you are younger (up to 27 years old) you'd pay even less (something like 500$).
EDIT: as pointed out by Pont's comment, in order to be able to travel with Interrail (different from Eurail or whatever) you have to be European citizen and one of the nations you would have to choose would be your homeland. Yet, even with a higher fare, it is still the best option.
Yes, the pass would be your best option. Even if you plan the whole trip a bunch of months in advance (most rail-companies do not allow to reserve places more than 6 months before the trip), consider that a regional ticket covering a one way journey from Salzburg to Munich (approx 150km) costs ~40$ CDN at least.
Since you'd have to cover a lot of km and don't have a lot of time, regional trains would not be the best option. Aside from Italy (high-speed trains are really cheap if you buy ticket in advance - source: I'm Italian) and maybe Spain, everywhere else is pretty much expensive (source: I don't live in Italy anymore), so the Interrail ticket really looks like the best choice.
BONUS (opinion based): As the comment from Greg points out, you really did overplan. Big cities like Rome, Paris and Berlin need at least 4 days / 3 nights to visit. In Barcelona it is worth to live the nightlife a bit (well, in Rome, Paris and Berlin too), so you may want to be flexible.